Abstract. We study Abelian generalized deformations of the usual product of polynomials
introduced in mp_arc/96-39. We construct an explicit example for the case of
$\frak{su}(2)$ which provides a tentative of a quantum-mechanical description
of Nambu Mechanics on ${\Bbb R}^3$. By introducing the notions of strong and
weak triviality of generalized deformations, we show that the Zariski product
is never trivial in either sense, while the example constructed here in a
quantum-mechanical context is only strongly non-trivial.